单调Wiener系统辨识的MINLIP
MINLIP for the Identification of Monotone Wiener Systems
摘要：
本文研究了由线性FIR动态模型和单调递增（或递减）静态函数组成的Wiener系统的MINLIP估计。给定$T$观测值，该算法归结为求解一个含$O(T)$变量和不等式约束的凸二次规划，实现了一种完全基于模型复杂度控制的推理技术.由此产生的估计的线性子模型被认为是几乎一致的，当没有噪声存在于数据中，在平滑的条件下的真正的非线性和本地持久性的激励（本地PE）的数据。这个结果是新颖的，因为它不依赖于经典的工具，作为一个“线性化”，使用泰勒分解，也不利用随机特性的数据。它表明如何扩展的方法，以应付嘈杂的数据，和经验证据对比性能的估计对其他最近提出的技术。
英文摘要：
This paper studies the MINLIP estimator for the identification of Wiener systems consisting of a sequence of a linear FIR dynamical model, and a monotonically increasing (or decreasing) static function. Given $T$ observations, this algorithm boils down to solving a convex quadratic program with $O(T)$ variables and inequality constraints, implementing an inference technique which is based entirely on model complexity control. The resulting estimates of the linear submodel are found to be almost consistent when no noise is present in the data, under a condition of smoothness of the true nonlinearity and local Persistency of Excitation (local PE) of the data. This result is novel as it does not rely on classical tools as a 'linearization' using a Taylor decomposition, nor exploits stochastic properties of the data. It is indicated how to extend the method to cope with noisy data, and empirical evidence contrasts performance of the estimator against other recently proposed techniques.
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